Preprints


  • Indeterminacy estimates and the size of nodal sets in singular spaces (with S. Farinelli). Submitted, arXiv:2011.04409

  • Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications (with A. Mondino). Submitted, arXiv:2004.08934.

  • Quantitative Obata’s Theorem (with A. Mondino and D. Semola). Submitted, arXiv:1910.06637.

Publications

  • The Globalization Theorem for the Curvature Dimension Condition (with E. Milman). Inventiones Math., arXiv:1612.07623.

  • Independence of synthetic Curvature Dimension conditions on transport distance exponent (with A. Akdemir, A. Colinet, R. J. McCann and F. Santarcangelo). Trans. Amer. Math. Soc., arXiv:2007.10980.

  • Displacement convexity of Entropy and the distance cost Optimal Transportation (with N. Gigli and F. Santarcangelo). Annales de la faculté des sciences de Toulouse, arXiv:2005.00243.

  • New formulas for the Laplacian of distance functions and applications (with A. Mondino). Analysis & PDE, arXiv:1803.09687.

  • Isoperimetric inequality under Measure-Contraction property (with F. Santarcangelo). J. Funct. Anal., 277 (2019), 2893-2917.

  • Quantitative isoperimetry à la Levy-Gromov (with F. Maggi and A. Mondino). Comm. Pure Appl. Math., LXXII (2019), 1631–1677.

  • A variational time discretization for the compressible Euler equations (with M. Sedjro and M. Westdickenberg). Trans. Amer. Math. Soc., 371 (2019), 5083-5155.

  • Almost euclidean Isoperimetric Inequalities in spaces satisfying local Ricci curvature lower bounds (with A. Mondino). Int. Math. Res. Not., 2020 (2020), 1481–1510.

  • Rigidity for critical points in the Levy-Gromov inequality (with F. Maggi and A. Mondino). Math. Z., (2018) 289: 1191.

  • An overview of L1 optimal transportation on metric measure spaces. Measure Theory in Non-Smooth Spaces, book chapter, edited by N. Gigli, De Gruyter Open.

  • Optimal maps in essentially non-branching spaces (with A. Mondino). Commun. Contemp. Math., 06 (2017) 19.

  • Isoperimetric inequalities for finite perimeter sets under lower Ricci curvature bounds (with A. Mondino). Rendiconti Lincei Matematica e Applicazioni, Volume 29, 3 (2018) 413–430.

  • Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds (with A. Mondino). Geom. Topol., 21 (2017) 603–645.

  • Tangent lines and Lipschitz differentiability spaces (with T. Rajala). Anal. Geom. Metr. Spaces, 4 (2016) 85–103.

  • Sharp and rigid isoperimetric inequalities in metric-measure spaces with lower Ricci curvature bounds (with A. Mondino). Inventiones Math., 208 (2017) 803–849.

  • Measure rigidity of Ricci curvature lower bounds (with A. Mondino). Advances Math., 286 (2016) 430–480.

  • A simple proof of global existence for the 1D Pressureless Gas Dynamics Equations (with M. Sedjro and M. Westdickenberg). SIAM J. Math. Anal., 47 (2015), no. 1, 66–79.

  • The polar cone of the set of monotone maps (with M. Westdickenberg). Proc. Amer. Math. Soc., 143 - 2 (2015), 781–787.

  • Decomposition of geodesics in the Wasserstein space and the globalization problem. Geom. Funct. Anal., Vol. 24 (2014) 493–551.

  • Monge problem in metric spaces with Riemannian curvature-dimension condition. Nonlinear Analysis, 99 (2014), 136–151.

  • A note on a residual subset of Lipschitz functions on metric spaces. Proceedings of Edinburgh Math. Society., Volume 58, Issue 3, 631–636.

  • Self-Intersection of Optimal geodesics (with M. Huesmann). Bull. London Math. Soc., 46 (2014) 653–656.

  • Existence and uniqueness of optimal transport maps (with M. Huesmann). Ann. I. H. Poincare ́ AN, 32 (2015) 1367–1377.

  • Local Curvature-Dimension condition implies Measure-Contraction property (with K.-T. Sturm). J. Funct. Anal., 262 (2012), 5110–5127.

  • Optimal transportation with branching distance costs and the obstacle problem. SIAM J. Math. Anal., Vol. 44 (2012), No. 1, 454–482.

  • The Monge problem for distance cost in geodesic spaces (with S. Bianchini). Commun. Math. Phys., 318 (2013), 615–673.

  • The Monge problem in the Wiener space. Calc. Var and PDE, Vol. 45 (1-2) (2012), 101–124.

Proceedings

  • The Monge problem in geodesic spaces (with S. Bianchini). The IMA Volumes in Mathematics and its Applications, Vol. 153, 217–234.